Question

Dolores made two isosceles right triangles by cutting the square along its diagonal. She says she can find the area of one of the triangles by using the formula for the area of the square, and then dividing the answer by 2. Do you agree? Explain.

Answer 1

Answer:   Yes, I agree. The explanation is given below.

Step-by-step explanation:  As given in the question, a square ABCD is shown in the attached figure. Dolores cut the square along its diagonal BD and made two isosceles right angled triangles ΔABD and ΔCBD.

We need to show the area of triangles ABD and CBD are equal, and half of the area of square ABCD, i.e.,

area of ΔABD = are of ΔCBD = half of area of square ABCD.

Now, in ΔABD and ΔCBD, we have

AB = CD,

AD = BC

and BD is the common side.

Therefore, by sing SSS (side-side-side) postulate, we get

ΔABD ≅ ΔCBD.

So, area of ΔABD = area of ΔCBD.

Now, area of square ABCD =  area of ΔABD + area of ΔCBD

                                              = 2 × area of ΔABD

                                              = 2 × area of ΔCBD.

Thus, Doroles is absolutely correct in finding the area of any one of the triangles by using the formula for the area of the square and then dividing by 2.

Hence explained.